It most certainly is deductive reasoning. You're using your memory to fill in the gaps in your perception. You saw me go behind that pillar, there's nowhere else I can go without you seeing me, therefore, I must still be there. You can call it whatever you want, but it absolutely is logic and deductive reasoning. You're skipping that step in the process. While that happens automatically for you, a less intelligent creature might not reach the same conclusion.
You can reach the same conclusion by using deductive reasoning, but it is
absolutely unnecessary. The deductive process would go something like this:
1. Creatures who move behind objects with nowhere else to go are still there.
2. That creature moved behind an object with nowhere else to go.
3 Therefore, that creature is still there.
Humans become capable of deductive reasoning in early adolescence, so according to your reasoning we shouldn't expect a creature less intelligent than a typical eleven year old to comprehend that the creature is still behind the pillar.
However, humans less than a year old are capable of understanding that objects continue to exist even when they can no longer be seen or heard. This is called
object permanence, and it doesn't require the use of logic at all. The mere fact that the creature existed before it went behind the pillar leads to the belief, or the assumption, that the creature continues to exist behind the pillar, which actually doesn't follow logically. The creature could, in fact, be anywhere, or actually cease to exist at all. Yet the brain learns to make this somewhat illogical leap in infancy because, through trial and error, the child develops a
sense of how objects behave. Logic, and especially deductive reasoning, come much later.
Your memory has nothing do do with your perception. At all.
Perhaps we're using different definitions of perception. Here's a description from Wikipedia that I think is quite nice:
Perception (from the Latin perceptio, percipio) is the organization, identification, and interpretation of sensory information in order to represent and understand the environment. All perception involves signals in the nervous system, which in turn result from physical or chemical stimulation of the sense organs. For example, vision involves light striking the retina of the eye, smell is mediated by odor molecules, and hearing involves pressure waves. Perception is not the passive receipt of these signals, but is shaped by learning, memory, expectation, and attention.
So you see that memory has
everything to do with the way we understand the raw sensory information we receive from our environment. Without that understanding, there really is no perception.
See here's the thing though. The lack of clear benefit doesn't necessarily mean there isn't any benefit. There could be possibilities. Like I mentioned earlier. Say I moved behind a pillar. There's no where for me to go, so I must still be there, according to you you still know my location. However, come around the pillar guess what, I'm not there! How did that happen?
What you didn't know is there was a secret door built into that pillar, and I ducked through it while I was obscured from your view. However, In order to do this undetected I must take the hide action. If I didn't, you would know I moved, because your other senses gave you clues.
Now, suppose you knew about the secret door and I did the same thing. I move behind the pillar and hide. Now, did I go through the secret door or not? You have no way of knowing, because your senses can't detect me. Situations like this is why it must be possible to hide, even if there is no clear way to move from the hiding spot. The hiding is not tied to the movement at all, as hiding is an action.
I understand what you're saying here about the timing of the Stealth check. The movements you're describing, however, are inextricably tied to the act of hiding. How would the character open and move through the secret door, and not be detected if she were not doing so stealthily? Those movements are the attempt at hiding that you are describing. That's when you should be making a Stealth check. What good is it to sneak quietly behind a pillar in full view of your enemies? You see, you're not hiding behind the pillar anymore. You're hiding inside the pillar, behind the secret door. Getting there is your attempt to hide.
Of course I'm not going to mess with the rule of cool, so in all sincerity, if this is fun for you, have at it.